New shell-model investigation of the lead-208 mass region: Spectroscopic properties and collectivity

Within the large-scale shell-model framework, an investigation of even-even nuclei in the vicinity of the ${}^{208}\mathrm{Pb}$ closed core is reported in the present work. The calculations of the low-lying state energies and the electromagnetic transitions of the Pb, Po, Rn, Ra, and Th nuclei with $126\le N\le 134$ are performed using a new effective interaction H208 derived from CD-Bonn nucleon-nucleon potential, through the $V_{\mathrm{low}\text{−}k}$ procedure. A special focus is devoted to the degree of the collectivity, where a transitional region from spherical nuclear shape to weakly collective behavior is revealed.

Figure 1

Experimental and theoretical energy levels of Pb isotopes.

Figure 2

Experimental and theoretical energy levels of Po isotopes.

Figure 3

Experimental and theoretical energy levels of Rn isotopes.

Figure 4

Experimental and theoretical energy levels of Ra isotopes.

Figure 5

Experimental and theoretical energy levels of Th isotopes.

Figure 6

The calculated $B(E2;2^{+}\to 0^{+})$ transitions of Pb, Po, Rn, Ra, and Th isotopes compared to the experimental data [20].

Figure 7

The calculated $B(E2;4^{+}\to 2^{+})$ transitions of Pb, Po, Rn, Ra, and Th isotopes compared to the experimental data [20].

Figure 8

The calculated $B(E2;6^{+}\to 4^{+})$ transitions of Pb, Po, Rn, Ra, and Th isotopes compared to the experimental data [20].

Figure 9

The calculated $B(E2;8^{+}\to 6^{+})$ transitions of Pb, Po, Rn, Ra, and Th isotopes compared to the experimental data [20].

Figure 10

Magnetic dipole moments of several nuclei calculated using the free (green line), the Arima (pink line), and the effective (blue line) spin and orbital $g$ factors compared to the data (red symbol) [20] (see text for more details).

Figure 11

Magnetic dipole moments of $2^{+},4^{+},6^{+}$, and $8^{+}$ states calculated using the effective $g$ factors and compared to the experimental data shown by the same symbol of different states with red color.

Figure 12

Ground state $E2$ invariants: the expectation values of quadrupole deformation $\langle Q^2\rangle$ (a) and triaxiality $\cos \left(3\gamma \right)$ (b).